We consider this extreme case, although it is unlikely to arise in practice, to demonstrate the robustness of the BAMG approach as a coarsening strategy for the targeted anisotropic problems.

When presenting results of the solver constructed by the resulting BAMG setup algorithm, we use two pre- and post-Gauss-Seidel relaxation sweeps on all grids except the coarsest, where a direct solver is used.

In this section, we illustrate the choice of coarse grids and interpolation patterns that the BAMG setup algorithm constructs when applied to the finite difference and bilinear finite element approximations of the anisotropic test problem for [epsilon] = [10.

Another interesting deliverable of the proposed BAMG setup algorithm, in particular of its implementation of the compatible relaxation and the algebraic distances, is the pattern of the resulting coarse-grid stencil.

In the tables, the asymptotic convergence rates [rho] of the two-grid solver produced by the BAMG setup algorithm are reported, along with the corresponding coarsening factors [[gamma].

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